Two conducting circular loops of radii `R_1 and R_2` are placed in the same plane with their centres coincidingt. Find the mutual inductane between them assuming `R_2ltltR_1`.

Explanation

Suppose a current I is established in the outer loop
The magnetic field at the centre will be ` B= (mu_0i)/(2R_1)`
As the radius R_2 of the inner coil is small compared to R_1, the flux of magnetic through it will be approximately `Phi = (mu_0i)/(2R_1) pir_2 ^2` so that the mutual inductance is `(m = (Phi)/(i) = (mu_0piR_2^2)/(2R_1)